Handbook of Conducting Polymers. Conjugated Polymers_ Theory, Synthesis, Properties, And...

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Handbook of Conducting PolymersThird Edition

CONJUGATED POLYMERS

THEORY, SYNTHESIS, PROPERTIES,AND CHARACTERIZATION

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Terje A. Skotheim/Conjugated Polymers: Theory, Synthesis, Properties, and Characterization 43587_C000 Final Proof page ii 17.11.2006 11:17am

Handbook of Conducting PolymersThird Edition

CONJUGATED POLYMERS

Edited by

Terje A. Skotheim and John R. Reynolds

THEORY, SYNTHESIS, PROPERTIES,AND CHARACTERIZATION

Terje A. Skotheim/Conjugated Polymers: Theory, Synthesis, Properties, and Characterization 43587_C000 Final Proof page iii 17.11.2006 11:17am

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Library of Congress Cataloging-in-Publication Data

Conjugated polymers : theory, synthesis, properties, and characterization / [edited by] Terje A. Skotheim, John R. Reynolds.

p. cm.Rev. ed. of: Handbook of conducting polymers. 2nd ed., rev. and expanded. c1998.Includes bibliographical references and index.ISBN-13: 978-1-4200-4358-7ISBN-10: 1-4200-4358-71. Conjugated polymers. 2. Conducting polymers. 3. Organic conductors. I. Skotheim, Terje A.,

1949- II. Reynolds, John R., 1956- III. Handbook of conducting polymers.

QD382.C66H36 2006547.70457--dc22 2006032904

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Dedication

This book is dedicated to our spouses, Ellen Skotheim andDianne Reynolds. Without their understanding and support,

we would never have completed this project.

Terje A. Skotheim/Conjugated Polymers: Theory, Synthesis, Properties, and Characterization 43587_C000 Final Proof page v 17.11.2006 11:17am

Acknowledgments

If this

Handbook

fulfills our hope that it makes a significant contribution to understanding the importanceof the field of conducting polymers, it is due to the enthusiastic participation of the many authors andthe outside reviewers. We want to extend our sincere thanks to all of them, and a special thank you tothe staff and editors at Taylor & Francis for their effort and assistance in bringing this project to asuccessful conclusion. Finally, and especially, this book is dedicated to our spouses, Ellen Skotheim andDianne Reynolds. Without their understanding and support, we could never have completed this project.

43609_ACK p. VI Page i Thursday, April 3, 2008 8:21 AM

Preface to ThirdEdition

The field of conjugated, electrically conducting, and electroactive polymers continues to grow. Since the

publication of the second edition of the Handbook of Conducting Polymers in 1998, we have witnessed

broad advances with significant developments in both fundamental understanding and applications,

some of which are already reaching the marketplace.

It was particularly rewarding to see that in 2000, the Nobel Prize in chemistry was awarded to Alan Heeger,

Alan MacDiarmid, and Hideki Shirakawa, recognizing their pathbreaking discovery of high conductivity in

polyacetylene in 1977. This capstone to the field was celebrated by all of us as the entire community has

participated in turning their initial discovery into the important field that it now is, almost 30 years later. The

vast portfolio of new polymer structures with unique and tailored properties and the wide range of

applications being pursued are far beyond what we could have envisioned when the field was in its infancy.

It was developments in polymer synthesis that led to free-standing polyacetylene films and the discovery

of conductivity in polymers. The synthesis ofp-conjugated chains is central to the science and technology

of conducting polymers and is featured in this edition. Examining the synthetic advances across the board,

one is struck by refined and careful syntheses that have yielded polymers with well-controlled and well-

understood structures. Among other things, it has led to materials that are highly processable using

industrially relevant techniques. In aspects of processing, spin coating, layer-by-layer assembly, fiber

spinning, and the application of printing technology have all had a big impact during the last 10 years.

Throughout the Handbook, we notice that structureproperty relationships are now understood and

have been developed for many of the polymers. These properties span the redox, interfacial, electrical,

and optical phenomena that are unique to this class of materials.

During the last 10 years, we have witnessed fascinating developments of a wide range of commercial

applications, in particular, in optoelectronic devices. Importantly, a number of polymers and composi-

tions have been made available by the producers for product development. This has helped to drive the

applications developments to marketable products.

While conductivity, nonlinear optics, and light emission continue to be important properties for

investigation and have undergone significant developments as discussed throughout the Handbook, the

advances in semiconducting electronics, memory materials, photovoltaics (solar cells), and applications

directed to biomedicine are emerging as future growth areas.

As we have assembled this edition, it has become clear that the field has reached a new level of

maturity. Nevertheless, with the vast repertoire of synthetic chemistry at our disposal to create new

structures with new, and perhaps unpredictable properties, we can expect exciting discoveries to

continue in this dynamic field.

Terje A. Skotheim

Tucson, Arizona

John R. Reynolds

Gainesville, Florida

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Editors

Terje A. Skotheim is the founder and chief executive of Intex, a Tucson, Arizona technology company.

Dr. Skotheim is an experienced developer of several technologies, a seasoned executive, and a successful

founder of several startup companies in the United States, Norway, and Russia. His research interests

over more than 25 years span several disciplines in materials science and applications, including

electroactive and conjugated polymers, molecular electronic materials, solid-state ion conductors, new

electronic nanoamorphous carbon- and diamond-like carbon materials, and thin-film and surface

science. He has pursued a wide range of technology applications of advanced materials in OLEDs,

biosensors, lithium batteries, photovoltaic cells, and MEMS devices. He has held research positions in

France, Sweden, and Norway in addition to the United States and was head of the conducting polymer

group at Brookhaven National Laboratory before launching his career as an entrepreneur.

Skotheim received his B.S. in physics from the Massachusetts Institute Technology and Ph.D. in

physics from the University of California at Berkeley (1979). He is the editor=coeditor of the Handbook

of Conducting Polymers (first and second editions, Marcel Dekker) and Electroresponsive Molecular and

Polymeric Systems (Marcel Dekker), the author of more than 300 publications and more than 70 patents.

He can be reached at [email protected].

John R. Reynolds is a professor of chemistry at the University of Florida with expertise in polymer

chemistry. He serves as an associate director for the Center for Macromolecular Science and Engineer-

ing. His research interests have involved electrically conducting and electroactive-conjugated polymers

for over 25 years with work focused on the development of new polymers by manipulating their

fundamental organic structure in order to control their optoelectronic and redox properties. His

group has been heavily involved in the areas developing new polyheterocycles, visible, and infrared

(IR) light electrochromism, along with light emission from polymer and composite light-emitting

diodes (LEDs) (both visible and near-IR) and light-emitting electrochemical cells (LECs). Further

work is directed to using organic polymers and oligomers in photovoltaic cells.

Reynolds obtained his M.S. (1982) and Ph.D. (1984) degrees in polymer science and engineering from

the University of Massachusetts. He has published more than 200 peer-reviewed scientific papers and

served as coeditor of the Handbook of Conducting Polymers that was published in 1998. He can be

reached by e-mail at [email protected] or see http:==www.chem.ufl.edu=reynolds=.

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Contributors

Kazuo Akagi

Department of Polymer Chemistry

Graduate School of Engineering

Kyoto University

Kyoto, Japan

A.N. Aleshin

School of Physics and Nano Systems Institute

National Core Research Center

Seoul National University

Seoul, Korea and A.F. Ioffe PhysicalTechnical

Institute

Russian Academy of Sciences

St. Petersburg, Russia

P. Audebert

Laboratory Photophysique & Photochimie

Supramoleculaires et Macromoleculaires

Ecole Normale Superieure de Cachan

Cachan, France

David Beljonne

Laboratory for Chemistry of Novel Materials and

Center for Research in Molecular Photonics

and Electronics

University of Mons-Hainaut

Mons, Belgium

and

School of Chemistry and Biochemistry

and Center for Organic Photonics and

Electronics

Georgia Institute of Technology

Atlanta, Georgia

Philippe Blanchard

Groupe Syste`mes Conjugues Lineaires

Laboratoire CIMMA, UMR CNRS 6200

Universite dAngers

Angers, France

Jean-Luc Bredas


and Center for Organic Photonics

and Electronics


Atlanta, Georgia

and

Laboratory for Chemistry of Novel Materials

and Center for Research in Molecular

Photonics and Electronics


Mons, Belgium

Thomas M. Brown

FREEnergy Laboratory

Department of Electronic Engineering

University of RomeTor Vergata

Rome, Italy

Uwe H.F. Bunz



Atlanta, Georgia

Franco Cacialli

Department of Physics and Astronomy and

London Centre for Nanotechnology

University College London

London, United Kingdom

Seung Hyun Cho

Polymer Technology Institute

Sungkyunkwan University

Kyunggi-do, Korea

and

Department of Organic Materials Engineering


Kyunggi-do, Korea

Terje A. Skotheim/Conjugated Polymers: Theory, Synthesis, Properties, and Characterization 43587_C000 Final Proof page xi 17.11.2006 11:17am

Jerome Cornil


and Center for Research in Molecular Photonics

and Electronics


Belgium

and

School of Chemistry and Biochemistry and Center

for Organic Photonics and

Electronics


Atlanta, Georgia

Veaceslav Coropceanu


for Organic Photonics and Electronics, Georgia

Institute of Technology

Atlanta, Georgia

X. Crispin

Department of Science and Technology (ITN)

Linkoping University

Norrkoping, Sweden

Aubrey L. Dyer

The George and Josephine Butler Polymer

Research Laboratories

Department of Chemistry and Center for

Macromolecular Science and Engineering

University of Florida


Arthur J. Epstein

The Ohio State University

Columbus, Ohio

M. Fahlman

Department of Science and Technology (ITN)


Norrkoping, Sweden

Pierre Fre`re



Universite dAngers

Angers, France

R. Friedlein

Department of Physics (IFM)


Linkoping, Sweden

Victor Geskin

Laboratory for Chemistry of Novel Materials and

Center for Research in Molecular Photonics

and Electronics


Mons, Belgium

G. Greczynski



Linkoping, Sweden

Andrew C. Grimsdale

School of Chemistry

Bio21 Institute

University of Melbourne

Parkville, Australia

Andrew B. Holmes

School of Chemistry

Bio21 Institute

University of Melbourne

Parkville, Australia

Jiaxing Huang

Miller Institute for Basic Research

in Science

University of California

Berkeley, California

and Department of Chemistry


Los Angeles, California

Malika Jeffries-El

Department of Chemistry

Iowa State University

Ames, Iowa

and


Carnegie Mellon University

Pittsburgh, Pennsylvania

M.P. de Jong



Linkoping, Sweden

Terje A. Skotheim/Conjugated Polymers: Theory, Synthesis, Properties, and Characterization 43587_C000 Final Proof page xii 17.11.2006 11:17am

Richard B. Kaner

Department of Chemistry and Biochemistry

and California NanoSystems Institute


Los Angeles, California

Stephan Kirchmeyer

H.C. Starck GmbH & Co. KG

Leverkusen, Germany

O. Korovyanko

Chemistry Division

Argonne National Laboratory

Argonne, Illinois

and

Department of Physics

University of Utah

Salt Lake City, Utah

Roberto Lazzaroni


and Center for Research in Molecular Photonics

and Electronics


Mons, Belgium

and

School of Chemistry and

Biochemistry and Center for Organic Photonics

and Electronics


Atlanta, Georgia

Philippe Lecle`re

Laboratory for Chemistry of Novel

Materials and Center for Research in

Molecular Photonics and Electronics


Mons, Belgium

Jun Young Lee

Polymer Technology Institute


Kyunggi-do, Korea

and

Department of Organic Materials Engineering


Kyunggi-do, Korea

Philippe Leriche



Universite dAngers

Angers, France-

Emil Jachim Wolfgang List

Christian Doppler Laboratory Advanced

Functional Materials

Institute of Solid State Physics

Graz University of Technology

Graz, Austria

and

Institute of Nanostructured Materials and

Photonics

Weiz, Austria

Richard D. McCullough


Carnegie Mellon University

Pittsburgh, Pennsylvania

Fabien Miomandre

Laboratory Photophysique & Photochimie

Supramoleculaires et Macromoleculaires

Ecole Normale Superieure de Cachan

Cachan, France

W. Osikowicz



Linkoping, Sweden

Y.W. Park

School of Physics and Nano Systems Institute

National Core Research Center

Seoul National University

Seoul, Korea

Martin Pomerantz

Center for Advanced Polymer Research


and Biochemistry

The University of Texas

Arlington, Texas

Seth C. Rasmussen

Department of Chemistry and

Molecular Biology

North Dakota State University

Fargo, North Dakota

Terje A. Skotheim/Conjugated Polymers: Theory, Synthesis, Properties, and Characterization 43587_C000 Final Proof page xiii 17.11.2006 11:17am

Knud Reuter

H.C. Starck GmbH & Co. KG

Leverkusen, Germany

John R. Reynolds

The George and Josephine Butler Polymer

Research Laboratories

Department of Chemistry and Center

for Macromolecular Science and Engineering



Jean Roncali



Universite dAngers

Angers, France

W.R. Salaneck



Linkoping, Sweden

Kirk S. Schanze




Ullrich Scherf

Bergische Universitat Wuppertal

Macromolecular Chemistry

Group and Institute for Polymer Technology

Wuppertal, Germany

Venkataramanan Seshadri


and the Polymer Program

University of Connecticut

Storrs, Connecticut

Demetrio A. da Silva Filho


for Organic Photonics and Electronics


Atlanta, Georgia

Jill C. Simpson

Crosslink

St. Louis, Missouri

Ki Tae Song

Electronic Chemical Materials Division

Cheil Industries Inc.

Kyunggi-do, Korea

Gregory A. Sotzing

Department of Chemistry and the

Polymer Program

University of Connecticut

Storrs, Connecticut

Sven Stafstrom

Department of Physics and

Measurement Technology, IFM


Linkoping, Sweden

Z. Valy Vardeny


University of Utah

Salt Lake City, Utah

Francis J. Waller

Air Products and Chemicals Inc.

Allentown, Pennsylvania

Michael J. Winokur


University of Wisconsin

Madison, Wisconsin

Xiaoyong Zhao




Terje A. Skotheim/Conjugated Polymers: Theory, Synthesis, Properties, and Characterization 43587_C000 Final Proof page xiv 17.11.2006 11:17am

Table of Contents

I: Theory of Conjugated Polymers

1. On the Transport, Optical, and Self-Assembly Properties of

p-Conjugated Materials: A Combined Theoretical=Experimental Insight.............................. 1-3

David Beljonne, Jerome Cornil, Veaceslav Coropceanu,

Demetrio A. da Silva Filho, Victor Geskin, Roberto Lazzaroni,

Philippe Lecle`re, and Jean-Luc Bredas

2. Theoretical Studies of ElectronLattice Dynamics in Organic Systems .................................. 2-1

Sven Stafstrom

II: Synthesis and Classes of Conjugated Polymers

3. Helical Polyacetylene Synthesized in Chiral Nematic Liquid Crystal ...................................... 3-3

Kazuo Akagi

4. Synthesis and Properties of Poly(arylene vinylene)s ................................................................. 4-1

Andrew C. Grimsdale and Andrew B. Holmes

5. Blue-Emitting Poly(para-Phenylene)-Type Polymers ................................................................ 5-1

Emil Jachim Wolfgang List and Ullrich Scherf

6. Poly(paraPhenyleneethynylene)s and Poly(aryleneethynylenes):

Materials with a Bright Future.................................................................................................... 6-1

Uwe H.F. Bunz

7. Polyaniline Nanofibers: Syntheses, Properties, and Applications............................................. 7-1

Jiaxing Huang and Richard B. Kaner

8. Recent Advances in Polypyrrole .................................................................................................. 8-1

Seung Hyun Cho, Ki Tae Song, and Jun Young Lee

9. Regioregular Polythiophenes ....................................................................................................... 9-1

Malika Jeffries-El and Richard D. McCullough

10. Poly(3,4-Ethylenedioxythiophene)Scientific Importance,

Remarkable Properties, and Applications ................................................................................ 10-1

Stephan Kirchmeyer, Knud Reuter, and Jill C. Simpson

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11. Thienothiophenes: From Monomers to Polymers ................................................................... 11-1

Gregory A. Sotzing, Venkataramanan Seshadri, and Francis J. Waller

12. Low Bandgap Conducting Polymers ......................................................................................... 12-1

Seth C. Rasmussen and Martin Pomerantz

13. Advanced Functional Polythiophenes Based on Tailored Precursors..................................... 13-1

Philippe Blanchard, Philippe Leriche, Pierre Fre`re, and Jean Roncali

14. StructureProperty Relationships and Applications of Conjugated

Polyelectrolytes ........................................................................................................................... 14-1

Kirk S. Schanze and Xiaoyong Zhao

III: Properties and Characterization of Conjugated Polymers

15. InsulatorMetal Transition and Metallic State in Conducting Polymers .............................. 15-3

Arthur J. Epstein

16. One-Dimensional Charge Transport in Conducting Polymer Nanofibers............................. 16-1

A.N. Aleshin and Y.W. Park

17. Structure Studies of p- and s-Conjugated Polymers ............................................................. 17-1

Michael J. Winokur

18. Electrochemistry of Conducting Polymers ............................................................................... 18-1

P. Audebert and Fabien Miomandre

19. Internal Fields and Electrode Interfaces in Organic Semiconductor Devices:

Noninvasive Investigations via Electroabsorption ................................................................... 19-1

Thomas M. Brown and Franco Cacialli

20. Electrochromism of Conjugated Conducting Polymers .......................................................... 20-1

Aubrey L. Dyer and John R. Reynolds

21. Photoelectron Spectroscopy of Conjugated Polymers ............................................................. 21-1

M.P. de Jong, G. Greczynski, W. Osikowicz, R. Friedlein, X. Crispin, M. Fahlman,

and W.R. Salaneck

22. Ultrafast Exciton Dynamics and Laser Action in p-Conjugated Semiconductors................ 22-1

Z. Valy Vardeny and O. Korovyanko

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ITheory ofConjugatedPolymers

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1On the Transport,

Optical, andSelf-Assembly

Properties ofp-Conjugated Materials:

ACombinedTheoretical=Experimental Insight

David Beljonne,Jerome Cornil,Veaceslav Coropceanu,Demetrio A. da Silva Filho,

Victor Geskin,

Roberto Lazzaroni,

Philippe Lecle`re, and

Jean-Luc Bredas

1.1 Introduction......................................................................... 1-3

1.2 Electronic Coupling in Organic Semiconductors............. 1-5

1.3 Impact of Charge Injection on the Optical Propertiesof Conjugated Polymers ................................................... 1-11Methodological Aspects: HartreeFock vs. Density Functional

Theory . Optical Signature of Delocalized Interchain Polarons

1.4 Self-Assembly of Conjugated Polymers into Solid StateNanostructures................................................................... 1-22A Joint Experimental=Modeling Methodology . Self-Assembly

of Homopolymer Chains . Influence of the Side Groups .

Self-Assembly of Copolymers

1.5 Synopsis.............................................................................. 1-39

1.1 Introduction

As the third edition of this Handbook exemplifies, remarkable progress has been made over the past few

years in the field of organic electronics. In this chapter, we will review some of our recent efforts along

three directions:

1. The evaluation of the electronic couplings in organic semiconductors: The electronic coupling is an

important parameter that enters the description of charge transport in both the band regime and

hopping regime. We will describe recent results on the rubrene single crystal.

Rubrene, a tetraphenyl derivative of tetracene, has recently attracted much attention since hole

mobilities as high as 20 cm2=V s at room temperature have been reported. In addition, the temperature


1-3

dependent mobility around 300 K is indicative of band transport. These results are a priori surprising

since the presence of the phenyl substituents attached to the side of the tetracene backbone is expected to

lead to weak intermolecular interactions. We thus embarked on a theoretical investigation of the

interchain transfer integrals for holes and electrons in rubrene and compared the results obtained for

rubrene with those for pentacene and tetracene. It is found that the limited cofacial p-stack interactions

that are present in rubrene actually result in very efficient electronic couplings, which are consistent with

the setting up of a band regime at room temperature.

2. The impact of charge injection on the optical properties: Injection of charges into (disordered)

conjugated polymers is believed to induce local distortions of the geometric structure. Direct experi-

mental measurements of the geometric modifications occurring upon charge injection are scarce and

subject to controversy. An alternative, indirect, way to assess these deformations is to monitor the

resulting changes in optical absorption. Indeed, according to the seminal SuSchriefferHeeger (SSH)

model, addition of extra charges to the polymer chains is expected to lead to the formation of polarons,

the appearance of localized electronic levels inside the otherwise forbidden bandgap, and the emergence

of new optical transitions.

Here, the changes in geometric structure in the ionized state of isolated model oligomers have been

reexamined by means of high-level ab initio quantum-chemical approaches, performed at both the

HartreeFock (HF) and density functional theory (DFT) levels. While DFT is found to fully delocalize

the charge and the resulting geometric distortions independently of the size of the system, HF leads to

results that are consistent with the SSH picture, i.e., the formation of self-localized polarons. We show,

however, that the mere emergence in the optical spectrum of conjugated systems of new, low-lying

optical transitions upon charge injection is not necessarily indicative of polaron formation but is simply

a signature of the molecular nature of these materials (though their energetic positions and relative

intensities are quantitatively affected by the geometric and electronic relaxation taking place upon

charge injection).

We have also investigated the changes in optical properties in the case in which, in the presence of

increasing order, the excess charges would spread out over several neighboring chains. Optical signatures

for such delocalized polarons are shifts in the monomer-based transition energies together with the

appearance of a new charge-transfer (charge-resonance) transition in the far-infrared. Such changes have

been observed when going from regio-random polythiophene derivatives to the corresponding regio-

regular materials, which form ordered two-dimensional multilayer structures. Importantly, the more

ordered polythiophenes also show the highest charge carrier mobilities reported so far for conjugated

polymers. This again illustrates the critical impact of morphology on the electronic structure of

conjugated polymers and the resulting charge-transport properties; therefore, efforts to control the

morphology at the nanoscale form the basis for the last section of this chapter.

3. Self-assembly of conjugated polymer chains (oligomers, homopolymers, and random or block copoly-

mers): The solid state supramolecular organization of p-conjugated materials is described on the basis of

a joint experimental and theoretical approach. This approach combines atomic force microscopy (AFM)

measurements on thin polymer deposits, which reveal the typical microscopic morphologies, and

molecular modeling, which allows one to derive the models for chain packing that are most likely to

explain the AFM observations.

The conjugated systems considered here are based on fluorene and indenofluorene building blocks

(substituted with alkyl or more bulky side groups to provide solubility; in block copolymers, the

conjugated segments are attached to nonconjugated blocks such as polyethylene oxide). Films are

prepared from solutions in good solvents in order to prevent aggregation processes in solution.

Therefore, the morphology observed in the solid state is expected to result mostly from the intrinsic

self-assembly of the chains, with little specific influence of the solvent. In such conditions, the vast

majority of compounds shows deposits made of fibrillar objects, with typical width and height of a few

tens of nanometers and a few nanometers, respectively. These results indicate that a single type of

packing process, governed by the p-stacking of the conjugated chains, is at work. The prevalence of such

a type of packing is supported by theoretical simulations. Molecular mechanics (MM) and molecular


1-4 Conjugated Polymers: Theory, Synthesis, Properties, and Characterization

dynamics (MD) calculations show that the conjugated segments tend to form stable p-stacks. For the

block copolymer molecules, assemblies can organize themselves in either a head-to-tail or head-to-head

configuration. The former case appears to be most likely because it allows for significant coiling of the

nonconjugated blocks while maintaining the conjugated blocks in a compact, regular assembly. Such

supramolecular organization is likely responsible for the formation of the thin elementary ribbons,

which can further assemble into larger bundles. We explore some other molecular architectures leading

to the formation of untextured deposits. Finally, a clear correlation with the luminescence properties in

the solid state is established.

1.2 Electronic Coupling in Organic Semiconductors

The charge-transport properties of conjugated materials critically depend on the packing of the

molecules or chains and the degree of order in the solid state, as well as on the density of impurities

and structural defects. As a result, the measured mobility values can vary largely as a function of sample

quality [1]. In addition, in many instances, the mobility values are extracted from current or voltage

characteristics (which depend on the nature of the device used) on the basis of analytical expressions

often derived for inorganic semiconductors. This opens the way to variations and uncertainties in the

determination of the actual mobility of the charge carriers in organic-based devices. Moreover, as

recently shown by Blom and coworkers [2], the charge mobility can be a function not only of the

electric field applied across the organic layer but also of the charge carrier density. Thus, the measured

mobility values can vary with the experimental conditions under which the I=V curves are recorded.

In the absence of chemical and physical defects, the transport mechanism in both conducting

polymers and molecular single crystals results from a delicate interplay between electronic and elec-

tron-vibration (phonon) interactions [3]. The origin and physical consequences of such interactions

can be understood by simply considering the tight-binding Hamiltonian for noninteracting electrons

and phonons:

H X

m

mamam

X

mn

tmnaman

X

Q

hvQ(bQbQ 1=2) (1:1)

Here, am and am are the creation and annihilation operators, respectively, for an electron on lattice site

m (molecular unit or chain segment); bQ and bQ are the creation and annihilation operators for

a phonon with wavevector Q and frequency vQ; m is the electron site energy and tmn is the transfer

(electronic coupling) integral, both of which depend on vibrational and phonon coordinates. The

electron-vibration coupling arising from the modulations of the site energy is termed local coupling;

it is the key interaction in the (Holstein) small radius polaron model [4,5]. The second source is related

to the transfer integral tmn, which is a function of the spacing and relative orientations of adjacent

molecules (chain segments). The modulation of the transfer integrals by phonons (vibrations) is referred

to as nonlocal coupling; it leads to Peierls-type models, such as the SSH Hamiltonian [6]. Although

generalized HolsteinPeierls models are discussed in literature, it is generally believed that Peierls (SSH)-

type mechanisms dominate the charge-transport and optical properties of conjugated polymers (see

Section 1.3), while local coupling is more relevant for charge transport in molecular crystals as discussed

in this section.

In highly purified molecular single crystals such as pentacene, transport at low temperature can be

described within a band picture, as shown by Karl and coworkers [7]. As a general rule of thumb,

(effective) bandwidths of at least 0.1 eV are needed to stabilize a band regime [3], in which case the

positive or negative charge carriers are fully delocalized; their mobilities are a function of the width and

shape of the valence band (VB) or conduction band (CB), respectively, i.e., of the extent of electronic

coupling between adjacent oligomers and chains. In pentacene, low-temperature charge carrier

mobilities of up to 60 cm2=V s have been reported [8]. When temperature increases, the mobility


On the Transport, Optical, and Self-Assembly Properties of p-Conjugated Materials 1-5

progressively decreases as a result of scattering processes due mainly to lattice phonons, as is the case in

metallic conductors; transport can then be described on the basis of effective bandwidths that are

renormalized and smaller than the bandwidths obtained for a rigid lattice. At the temperature around

which localization energy becomes dominant vs. delocalization energy, transport crosses over to a ther-

mally assisted polaron hopping regime in which localized charge carriers jump between adjacent chains.

At the microscopic level, polaron hopping can be viewed as a self-exchange electron-transfer reaction

where a charge hops from an ionized oligomer or chain segment to an adjacent neutral unit. In the

framework of semiclassical Marcus theory, the electron-transfer rate is written as

kET 4p2

ht2

14plkT

p exp (l DG)2

4lkT

(1:2)

The transfer rate depends on two important parameters:

1. The electronic coupling, which reflects the strength of the interactions between adjacent chains

and needs to be maximized to increase the rate of electron transfer, i.e., of charge carrier

hopping; in the present context, the electronic coupling is often assimilated to the transfer

integral, t, between adjacent chains.

2. The reorganization energy, l, which needs to be minimized; in an ultra-pure single crystal,

a lower l means a higher temperature for the crossover to a hopping regime. The reorganization

energy is made up of two components: an inner contribution, which reflects the changes in the

geometry of the molecules or chain segments when going from the charged state to the neutral

state and vice versa; and and an outer contribution, which includes the changes in the polar-

ization of the surrounding medium upon charge transfer.

It is useful to note that the reorganization energy, l, is directly related to the (Holstein) polaron binding

energy (Epol l=2) [9,10]; in addition, for a self-exchange reaction, the driving force DG8 is zero.Since an in-depth discussion of the nature and magnitude of the reorganization energy has been

presented in a recent review [9], we will focus in this chapter on the electronic coupling between

adjacent p-conjugated chains and describe some recent developments.

The transfer integrals quantify the electronic coupling between two interacting oligomers or chain

segments, Ma and Mb, and are defined by the matrix element t hCijVjCfi, where the operator Vdescribes the intermolecular interactions and Ci and Cf are the wavefunctions corresponding to the two

charge-localized states {Ma Mb} and {Ma Mb} [or {Ma Mb} and {Ma Mb }], respectively.

A number of computational techniques, based on ab initio or semiempirical methodologies, have been

developed to estimate the electronic coupling t; they have recently been reviewed in several excellent

publications [1113]. The most simple and still reliable estimate of t is based on the application of

Koopmans theorem [11]. In this context, the absolute value of the transfer integral for electron [hole]

transfer is approximated by the energy difference, t (L 1[H]L[H1])=2, where L[H] and L 1[H1]are the energies of the LUMO and LUMO 1 [HOMO and HOMO 1] orbitals taken from theclosed-shell configuration of the neutral state of a dimer {Ma Mb}. The sign of t can be obtained fromthe symmetry of the corresponding frontier orbitals of a dimer [14]; t is negative if the LUMO [HOMO]

of the dimer {Ma Mb} is symmetric (i.e., represents a bonding combination of the monomer LUMOs[HOMOs]), and positive if the LUMO [HOMO] is asymmetric (antibonding combination of the

monomer LUMO [HOMO]s).

These considerations explain that many theoretical studies have made use of Koopmans theorem to

estimate electronic couplings [1521]. However, caution is required when using Koopmans theorem

to estimate transfer integrals in asymmetric dimers. In such instances, part of the electronic splitting can

simply arise from the different local environments experienced by the two interacting molecules, which

create an offset between their HOMO and LUMO levels. In order to evaluate the actual couplings, this

offset needs to be accounted for, either by performing calculations using molecular orbitals localized on

the individual units as the basic set [22], by computing directly the coupling matrix element between the



molecular orbitals of the isolated molecules, or by applying an electric field to induce resonance between

the electronic levels, as done by Jortner and coworkers [19]. In this chapter, we will consider cases in

which these site energy fluctuations are small and can thus be neglected.

The electronic splittings reported below have been calculated within Koopmans theorem using the

semiempirical HF intermediate neglect of differential overlap (INDO) method; interestingly, the INDO

method provides transfer integrals of the same order of magnitude as those obtained with DFT-based

approaches [23,24]. It is also interesting to note that when building (infinite) one-dimensional stacks of

molecules, oligomers, or chains, the widths of the corresponding VBs and CBs are usually found to be

nearly equal to four times their respective t integrals; when this is the case, it indicates that the tight-

binding approximation is relevant (which is not surprising, since transfer integrals are short-ranged and

hence interactions with non-nearest neighbors can often be neglected).

Before turning to actual packing structures, we recall that our simple analysis of perfectly cofacial

configurations has shown that [3,25]:

1. By their very nature, cofacial configurations provide the largest electronic interactions (coup-

ling) between adjacent chains.

2. As a qualitative rule, the lower the number of nodes in the wavefunction of the frontier level of

an isolated chain, the larger the splitting of that level upon cofacial interaction.

3. In cofacial stacks of oligomers, the valence bandwidth is expected to be larger for small oligomers

and the conduction bandwidth, larger for long oligomers; however, for any oligomer length, the

valence bandwidth remains larger than the conduction bandwidth. The latter point is the basic

reason why it was conventionally thought that organic materials displayed higher hole mobilities

than electron mobilities. For actual packing structures, this belief has no reason to hold [3,4].

The high quality of rubrene crystals has allowed detailed measurements of the transport characteristics,

including the recent observation of the Hall effect [26]. Charge transport in rubrene single crystals, while

trap-limited at low temperature, appears to occur via delocalized states over the 150300 K temperature

range with an (anisotropic) hole mobility of up to 20 cm2=V s at room temperature [27,28].

Due to the bulky phenyl substituents attached to the side of the tetracene backbone (see Figure 1.1),

weak intermolecular interactions are a priori expected in rubrene. The large carrier mobilities that are

observed are thus surprising from that standpoint. Therefore, in order to elucidate the origin of these

mobilities and of their marked anisotropy along the crystallographic axes, we have performed quantum-

chemical calculations of the electronic structure of rubrene [29]; we discuss the results of these

calculations below and also make comparisons of tetracene and pentacene.

In the isolated (neutral) molecules, the shapes and energies of the HOMO and LUMO levels of

rubrene and tetracene are very similar (see Figure 1.2). This reflects the large torsion angle between the

phenyl rings and the tetracene backbone in rubrene (this angle is calculated in the isolated molecule and

measured in the crystal [30] to be 858). This near-perpendicular arrangement strongly reduces anymixing of the molecular orbitals between the backbone and the side groups.

The widths of the HOMO and LUMO bands, cal-

culated at the INDO level, are plotted in Figure 1.3 as

a function of cos(p=N1), where N is the number ofrubrene molecules in stacks built along the a-direction

and d-direction (see Figure 1.4). Large transfer inte-

grals are found along the a-direction and lead to

bandwidths W of 340 and 160 meV for holes andelectrons, respectively. Smaller interactions are calcu-

lated along the diagonal directions (d ), while all other

directions provide for negligible transfer integrals.

Interestingly, the highest bandwidths in rubrene

(along the a-direction) are comparable to the highest

bandwidths calculated in pentacene (along the diag-

FIGURE 1.1 Chemical structures of (a) tetra-

cene and (b) rubrene.



onal d-directions) [25,31]. The linear evolution of the calculated bandwidths (Figure 1.3) as a function

of cos(p=N1) implies that the intermolecular interactions in rubrene can be cast into a tight-bindingformalism, with W 4t, as was also observed for oligoacenes, sexithiophene, and bisdithienothiophene[3133].

To understand the magnitude of the transfer integral values, we need to examine the packing of

the molecules in the crystal structure. Both rubrene and pentacene (or tetracene) present a herringbone

motif in the ab plane where the most significant electronic couplings are found. However, there are major

differences that are triggered by the presence of the phenyl side groups in rubrene:

FIGURE 1.2 DFT-B3LYP=6-31G(d,p)-calculated HOMO and LUMO wavefunctions in the neutral ground state

geometry: (a) tetracene HOMO (4.87 eV); (b) rubrene HOMO (4.69 eV); (c) tetracene LUMO (2.09 eV); and(d) rubrene LUMO (2.09 eV).

0.00

50

100

150

Splitt

ing

(meV

)

200

250

300

350HOMOdLUMOdHOMOaLUMOa

0.2 0.4 0.6cos(/(N + 1))

0.8 1.0

FIGURE 1.3 Evolution as a function of cos(p=N1) of the INDO-calculated splitting formed by the HOMO andLUMO levels in rubrene stacks along the a-direction and d-direction. N is the number of interacting molecules.

A linear fit was used to extrapolate the full bandwidth along each stack. The calculated valence (conduction)

bandwidth is 341 meV (159 meV) along the a-direction and 43 meV (20 meV) along the d-direction. The

bandwidths along other directions are vanishingly small and therefore not reported.



1. The long molecular axes all come out of the ab plane in pentacene (or tetracene), while in

rubrene they are embedded in that plane (see Figure 1.4). As a consequence, the long molecular

axes of adjacent molecules along the diagonal (herringbone) directions are parallel in pentacene,

while they are almost perpendicular in rubrene. This explains the smaller transfer integrals along

the diagonal directions in rubrene.

2. Along the crystal a-direction for which the highest bandwidths are calculated, the rubrene

molecules are found to form a p-stack with a stacking distance of 3.74 A; although this distance

is larger than in a typical p-stack [34,35], a major feature is that there occurs no displacement

along the short molecular axes (see Figure 1.4). In pentacene (or tetracene), the short-axis

displacements are so large that adjacent molecules along a interact weakly in spite of a very short

p-stack distance of 2.59 A.

While there occurs no short-axis displacement along the a-direction in rubrene, the phenyl side groups

promote a very large sliding, by 6.13 A, of one molecule with respect to the next along the long

(a)

(b)

3.74 6.13

d1

d2

a

b

d

d

a

b

FIGURE 1.4 Illustration of the lattice parameters within the ab layer of crystalline (a) pentacene and (b) rubrene.

The long-axis displacement and p-stacking distance in the a-direction are also indicated.



molecular axis (see Figure 1.4). This leads to the appearance of the slipped-cofacial configuration

illustrated in Figure 1.4. Such long-axis displacements are known to reduce the electronic coupling

between adjacent molecules. As noted above, the coupling is maximum for the perfectly cofacial

situation; it then oscillates between positive and negative values as a function of increasing displacement

and eventually vanishes for large displacements [9,25].

The question that needs to be answered is how such a pronounced long-axis sliding can be consistent

with the large bandwidths that are calculated along the a-direction of the rubrene crystal. To provide an

answer, we examined at the INDO level the evolution of the HOMO and LUMO transfer integrals for

a complex made of two tetracene molecules (we did not consider the phenyl side groups present in

rubrene since the phenyls do not play any significant role in the HOMO or LUMO wavefunctions of

rubrene (see Figure 1.2) and their presence would obviously lead to major steric interactions upon

displacement). We started from a perfectly cofacial situation with the two molecules superimposed at

a distance of 3.74 A, as in the rubrene crystal structure, and then increasingly displaced the top molecule

along the long molecular axis. The results are shown in Figure 1.5.

The HOMO and LUMO transfer integrals display a typical oscillating evolution upon displacement

[3,4]. The most remarkable result is that the displacement of 6.13 A observed in the rubrene crystal

actually closely corresponds to extrema in the oscillations of both HOMO and LUMO transfer integrals.

This result clarifies why, even at such a large long-axis displacement, the transfer integrals are still

a significant fraction of the values found for the cofacial case.

Along the d-direction of rubrene, the calculated HOMO and LUMO bandwidths are much smaller

than along the a-direction, in agreement with the experimental findings [36] that show a strong

anisotropy of the mobility within the herringbone planes of rubrene single crystals. Two adjacent

molecules in the b-direction are 14.4 A apart (see Figure 1.4); for such a distance, there is no electronic

overlap between the two oligomers. As a result, a charge carrier moving along the b-direction is expected

to have to make its way via the intercalated molecules (in the d-direction illustrated in Figure 1.4);

thus, the transfer integrals along the d-direction should be used to understand the transport in the

b-direction. This suggestion has been confirmed by the results of the calculation of the three-dimen-

sional electronic band structure of the rubrene crystal with the plane-wave (PW) DFT method [29].

0200

100

0

Tran

sfer

inte

gral

(meV

)

100

200

HOMOLUMO

300

2 4 6 8 10Displacement ()

Displacement

3.74

12 14

FIGURE 1.5 Evolution of the INDO HOMO and LUMO transfer integrals as a function of displacement, for

a complex made of two tetracenes stacked along the rubrene a-direction with a p-stacking distance of 3.74 A. The

dotted line indicates the magnitude of the long-axis displacement (6.13 A) found in the rubrene crystal. The

molecular geometries were optimized at the DFT-B3LYP=6-31G(d,p) level.



The PW-DFT results are also consistent with a rubrene valence bandwidth on the order of a few tenths

of an eV (ca. 0.4 eV). Thus, the INDO and DFT calculations concur to suggest that, in the absence of

traps, a band regime should be present in rubrene single crystals at low temperature which could still be

operative for holes at room temperature (as a consequence of larger electronic coupling for holes than

for electrons); the latter is consistent with the decrease in mobility with temperature observed around

room temperature [28,36].

1.3 Impact of Charge Injection on the Optical Propertiesof Conjugated Polymers

Charge injection into conducting polymers is readily achieved by (reversible) chemical or electrochem-

ical redox transformations and leads to drastic changes in their electrical [37] and optical [38]

properties. In particular, new optical transitions at lower energies than in the neutral polymer emerge

upon doping. The SSH theory [6,39] has shaped the early understanding of these phenomena.

With appropriate parameterization, the SSH Hamiltonian depicts neutral conjugated polymers as

semiconductors; the lowest optical transition is then interpreted as an electronic excitation from the

(fully occupied) VB to the (unoccupied) CB. When a conjugated polymer is brought into a charged state

(i.e., when it is doped), a few, typically two or three, new low-energy optical transitions are usually

observed (see Figure 1.8). These subgap states are the result of local geometric distortions due to charge

self-trapping (self-localization). In addition to the description of the characteristics of the ground state,

the SSH Hamiltonian reproduces the appearance of several types of excitations [40]: polarons (singly

charged species with spin 12); bipolarons (doubly charged species that are spinless); and, in the case of

degenerate ground state polymers such as trans-polyacetylene, solitons (either singly charged species

without spin or neutral species with spin 12). As a result of their electron-phonon origin, these excitations

are associated with well-defined (self)-localized charges and=or geometric distortion distributions.

In fact, conjugated polymers often present a distribution of finite chain lengths. Furthermore, the

conjugation lengths are rather short (typically 520 units), so that a molecular picture can also be

applied. Within such a molecular approach, it is interesting to note that, even in the absence of any

geometric and electronic relaxation upon ionization, new low-energy optical transitions would arise that

would involve the discrete level affected by electron removal or addition (see bottom of Figure 1.6).

1.3.1 Methodological Aspects: HartreeFock vs. Density Functional Theory

In order to study theoretically the electronic excited states and, therefore, the optical properties of

a charged conjugated chain, the molecular geometry is usually optimized beforehand. Thus, it is of

interest to assess: (i) the characteristics of the ionized state geometry; and (ii) to what extent the

calculated optical properties depend on the input molecular geometries. While the transport properties

can be well described in a one-electron picture by considering the calculated splitting of the HOMO or

LUMO levels (see above), excited states are generally not properly depicted at that level when consider-

ing simply the promotion of a single electron from an occupied molecular orbital to an unoccupied

orbital. It is possible to go beyond the one-electron picture by using a configuration interaction (CI)

technique; in this approach, excited states are described as a linear combination of electronic configur-

ations where one or several electrons are excited from various occupied to unoccupied molecular

orbitals. This is the underlying principle of the INDO=SCI calculations reported here, for which the

molecular orbitals are initially calculated at the INDO level and singly excited configurations are

involved in the CI expansion. The use of several electronic configurations is also exploited in time-

dependent (TD) formalisms, as is the case for the TD-DFT results discussed later.

To elaborate point (i), we chose thiophene oligomers as model systems [41]. In the present context, it

is convenient to characterize the geometry with a single relevant parameter, the inter-ring CC bond

length; this bond shortens in radical-cations in agreement with the valence-bond scheme shown in

Figure 1.7. The results of ab initio and semiempirical HF spin-restricted open-shell self-consistent field



(ROHF-SCF) calculations on oligothiophenes are in good mutual agreement. They indicate clear self-

localization of spin and charge over five to six rings around the middle of the chain, with the

accompanying quinoid geometric distortion being somewhat more confined. On the contrary, we

find, in agreement with previous studies [42,43], that the spin-unrestricted HF (UHF) tends to equalize

single and double bonds and to completely delocalize neutral radicals. This trend is completely reversed

when, starting from the UHF reference, geometry optimization is performed (on an oligomer long

enough to distinguish between polaron formation and charge delocalization) with a correlated ab initio

unrestricted second-order MollerPlesset (UMP2) method. A major result is that UMP2 significantly

sharpens the localization of the polaron with respect to all HF methods.

The treatment of the spin characteristics in all these methods is not entirely satisfactory. The ROHF

method insures a correct symmetry of the wavefunction but rules out spin polarization. On the other

hand, the UHF open-shell solutions for conjugated systems are usually spin-contaminated [41,44]. In

this context, DFT has emerged as an attractive option by providing for inclusion of both electron

correlation and spin polarization effects with usually low spin contamination. However, DFT calcula-

tions rapidly became a subject of controversy when applied to conjugated polymers. When a pure DFT

approach (e.g., the BLYP functional) is used in the case of a radical-cation, a complete charge=spin

delocalization is predicted to occur over the whole chain (Figure 1.7, see also [45,46]), which is in

marked contrast to the HF and MP2 results. A hybrid DFT approach (the BHandHLYP functional

including as much as 50% of HF exchange) yields a relatively diffuse defect for 8T, but with somedegree of localization of the polaron toward the middle of the chain at this chain length [41]. It is

interesting to note the absence of direct correlation between the degree of localization of geometry

distortion and charge=spin distribution that can occur: while the UHF geometric distortion is extended

(with intermediate bond lengths along the entire backbone), the UHF method yields localized charge

and spin distributions (Figure 1.7).

In addition, there is a notable difference in the chain-length evolution of the HF- and BHandHLYP-

optimized radical-cation structures [47]. With AM1 ROHF, self-localization occurs; this is first seen via

an increased localization as the chain becomes longer (Figure 1.8a) and, after a certain chain-length

threshold (decamer in this case), via symmetry breaking (the distortion is no longer forced to be in the

CB CB

Relaxation

CB

VB

e Relaxation LUMO (POL2)

SUMO (POL1)HOMO

e

VB

(a)

(b)

VB

FIGURE 1.6 Schematic representation of the electronic structure of conjugated polymers according to (a) band

theory and (b) a molecular picture.



middle of the chain) and independence of the polaron segment geometry vs. the rest of the chain

(Figure 1.8b). On the contrary, with hybrid DFT (Figure 1.8c), in spite of some degree of localization,

the defect still spreads somewhat more along the chain as the oligomer becomes longer and no

symmetry breaking is observed even for 13T .Similar geometric trends with HF and DFT methods were obtained by others and by our group

[48,49] in the case of oligophenylenevinylene (OPV) radical-cations. Thus, it can be concluded that: (i)

HF tends to localize the geometric distortion and the excess charge and spin; (ii) pure DFT with standard

functionals leads to moderate changes that extend over the entire molecule; and (iii) the behavior is

intermediate with hybrid DFT.

A brief discussion on the theoretical description of the structure of extended conjugated compounds

is in order at this stage. As is well established for neutral conjugated oligomers, and polyenes in

particular, taking electron correlation into account is crucial to obtain a correct degree of bond-length

alternation (BLA). While an ab initio HF approach strongly overestimates BLA, MP2 correlated results

are in good accord with experimental data. On the other hand, pure DFT functionals, even though they

take electron correlation into account, tend to underestimate BLA strongly; this feature is equally true

for the simplest LDA, the more precise GGA, and the more sophisticated meta-GGA families (see e.g.,

[50] for recent results, discussion, and references therein). The reason for the failure of common DFT

functionals was shown [51] to be the self-interaction error (noncancellation of Coulomb and exchange

terms for the same orbital), which is corrected only in rather exotic functionals. A practical, well-known

way to improve on DFT results is to include a part of HF exchange in the so-called hybrid DFT. For

polyenes in particular, a correct BLA is obtained with the popular B3LYP functional (which contains

20% of HF exchange). However, this is not a general rule; for polymethineimine, BLA is still underesti-

mated with B3LYP [52]. Thus, a correct BLA can in principle be obtained in neutral conjugated

oligomers within hybrid DFT, but the amount of required HF exchange is unknown beforehand.

1.50 8T+UHF/3-21G*ROHF/3-21G*

UB3LYP/3-21G*AM1/C14AM1/UHF

UMP2/3-21G*UBH&HLYP/3-21G*ROBH&HLYP/3-21G*1.48

1.46

1.44

ThT

h bo

nd le

ngth

()

1.42

1.40

1.38

(a)(b)

(c)

1 2 3 4 5

SS

S

0

S+

1+

6 7

0.30

0.25

0.20ROHF

BHandHLYP

UMP2UHF

0.15

Char

ge p

er ri

ng

0.10

0.05

0.400.350.300.250.20

Spin

per

ring

0.150.100.050.00

0.05

4 3 2

UMP2UHFROHF

BHandHLYP

1 1 2 3 4

FIGURE 1.7 (a) Inter-ring CC bond lengths, (b) Mulliken charge, and (c) spin distributions in the octathiophene

(8T ) radical-cation as obtained by geometry optimization with different methods.



The situation is still more complicated for open-shell (radical) conjugated oligomers. In neutral

polyene radicals, even the most precise and expensive ab initio correlated methods, such as CCSD(T),

can give at best a qualitative prediction of the spin density distributions, and the behavior of common

DFT schemes is also mediocre [42]. The problems with exchange and correlation are augmented in this

case by the spin-restricted=unrestricted ansatz dilemma discussed above. An efficient practical solution

is, somewhat unexpectedly, provided by correlated semiempirical methods with a simple Hamiltonian,

such as PPP [53]. We therfore also often use semiempirical methods in our studies of conjugated

oligomer radical-ions.

To get more insight into the effect of geometry on the optical properties, we now turn to an analysis of

the first optically allowed transition in OPV oligomers; this transition has a clear one-electron nature,the wavefunction of the associated excited state being dominated by the HOMO!SOMO (HOMO!POL1)excitation. Furthermore, this low-energy polaron transition has recently been singled out for the

universal character of its energy evolution in different conjugated polymers [54].

Figure 1.9 illustrates the shape of the HOMO orbital in the neutral 6-ring OPV and that of the SOMO

(POL1) in the unrelaxed (i.e., neutral) geometry and fully relaxed (i.e., singly charged) geometry, as

provided by INDO calculations on the basis of AM1 geometries. The HOMO of the neutral molecule is

concentrated near about the middle of the chain. Strong localization occurs for the SOMO (POL1) of the

unrelaxed radical-cation, which exhibits a bondingantibonding pattern very similar to the HOMO of

the neutral molecule. Interestingly, the geometry relaxation characteristic of the radical-cation adds

practically no modification to the shape of the SOMO (POL1) level (compare Figure 1.9b and Figure 1.9c).

It is usual in quantum chemistry to use different methods for geometry optimization and for the

subsequent determination of the molecular properties. In addition to the different geometries used as

input, we have therefore also applied different methods for the calculation of the optical transitions to

the electronic excited states, namely, INDO-SCI and time-dependent DFT (TD-DFT). Interestingly,

a Mulliken population analysis for the 7-ring OPV radical-cation, presented in Figure 1.10, demonstrates

1.45nT+ : AM1 C14 nT+ : AM1 C14

nT+ : UBH&HLYP/3-21G*

1.44

1.43

1.42

1.41

ThT

h bo

nd le

ngth

()

1.403T+

10T+11T+12T+13T+16T+

4T+5T+6T+7T+8T+9T+10T+

1.39

1.38

1.37

1.45

1.44

1.43

1.42

1.41

ThT

h bo

nd le

ngth

()

1.40

1.39

1.38

1.37

8T+9T+10T+13T+

1.45

1.44

1.43

1.42

1.41

ThT

h bo

nd le

ngth

()

1.40

1.39

1.38

1.37ThTh bond position

ThTh bond position

ThTh bond position(a) (b)

(c)FIGURE 1.8 Evolution of inter-ring CC bond lengths in thiophene oligomers as a function of chain length as

optimized with AM1-CAS (a) before and (b) after symmetry breaking and (c) with BHandHLYP=3-21G*.



that, irrespective of geometry, the excess charge is systematically sharply localized when INDO calcula-

tions are performed and weakly localized for hybrid DFT results. Thus, it appears that it is primarily the

choice of the method used for the electronic-structure calculations, rather than the molecular geometry,

that drives the theoretical evolution of the optical properties.

To better illustrate these trends, the chain-length evolution of the lowest transition energy, as

computed with different methods and different molecular geometries, is reported in Figure 1.11 for

the OPV radical-cations. At the INDO-SCI level, the transition energies obtained on the basis of the

AM1 geometries saturate quickly with increasing chain length and level off around OPV7-9. The same

saturation is observed when the radical-cations are forced to adopt the AM1 geometry of the neutral

OPV chains, except that the transition energies are red-shifted (by up to 0.4 eV for the longest

oligomers). The transition is strongly optically allowed, as indicated by the increase in the oscillator

strength from 0.47 to 1.31 throughout the series. A similar evolution is obtained for the transition

energies computed at the INDO-SCI level on the basis of pure DFT geometries. In contrast, the

transition energies calculated with the TD-DFT formalism for geometries obtained at the AM1 and

pure DFT (VWN-BP) levels evolve in a very different way: in both cases, there is hardly any sign of

saturation even for chain lengths as long as 89 repeat units.

The different curves in Figure 1.11 are crossing for oligomer lengths that typically correspond to the

longest chains investigated at the experimental level; therfore, the assessment of which is the most

reliable theoretical technique would actually require data collected for longer chains. Nevertheless, it is

clearly seen at the long-chain limit that the calculated transition energies decrease in the following order:

HF-CI==HF > HF-CI==DFT > TD-DFT==HF > TD-DFT==DFT (where the latter acronym represents the

method used for geometry optimizations and the former that used for electronic-structure calculations).

Combining DFT geometries with the TD-DFT formalism provides very low excitation energies in long

chains. The rapid saturation of the INDO-SCI transition energies suggests that the structure of

the frontier orbitals has already converged in short chains. The larger values calculated for the fully

FIGURE 1.9 Linear combination of atomic orbitals (LCAO) pattern of (a) the HOMO level in the neutral 6-ring

OPV; and the SOMO level of (b) unrelaxed and (c) fully relaxed 6-ring OPV, as calculated at the INDO level onthe basis of AM1-optimized geometries. The size and color of the circles reflect the amplitude and sign of the LCAO

coefficients, respectively.



relaxed radical-cations compared to the unrelaxed systems point to a reinforcement of the electronic

localization. The AM1==INDO-SCI values, which saturate around 0.80.9 eV, provide the best agreement

with the experimental value initially reported for doped PPV (1 eV) [38]; the other theoretical valuessaturate more slowly with chain length and are too low in energy or, even worse, do not seem to saturate

at all. Recent studies based on vis-NIR spectroscopy of chemically doped PPV [55] and on photoinduced

absorption in a series of phenylenevinylene oligomers [56] indicate a somewhat smaller first polaron

transition energy of 0.6 eV.To provide a more general assessment of the TD-DFT results, it is worth noting that, while it usually

gives accurate results for excitation energies, the method is known to fail for higher electronic states with

doubly excited charge-transfer or Rydberg character, and for excitations in extended p-systems [57].

0.25

0.20

0.15

0.10

0.05

0.00

(a)

(b)

0.25

0.20

0.15

0.10

0.05

0.00

Ph Ph Ph Ph Ph Ph PhVi Vi Vi Vi Vi Vi

Ph Ph Ph Ph Ph Ph PhVi Vi Vi Vi Vi Vi

7PPV+

7PPV+

AM1 geometryBH&HLYP geometryBLYP geometry

AM1 geometryBH&HLYP geometryBLYP geometry

BH&H

LYP

Mul

liken

cha

rge

per u

nit

IND

O M

ullik

en c

harg

e pe

r uni

t

FIGURE 1.10 Charge distribution on the phenylene and vinylene units of the 7-ring OPV, as obtained with the(a) hybrid DFT-BH and HLYP and (b) INDO methods for various starting geometries.



In practice, it is not always easy to know how to classify a given excited state. In the case discussed above,

the first excited state is a valence single excitation with no charge-transfer character. Although the

polaron MOs are localized in the central segment of the chain, their extension increases with chain

length, which can be related to DFT favoring delocalization. In turn, this can lead to a progressive

underestimation of the excitation energy. The quality of the TD-DFT description is expected to become

worse for longer oligomers.

The chain-length evolution of the lowest transition energy is calculated to depend primarily on the

degree of electronic localization of the SOMO (POL1) level; the latter is to a large extent decoupled from

the details of the actual geometry, making the calculated results mostly dependent on the nature of the

theoretical method used to generate the electronic structure. In the range of oligomer sizes typically

studied experimentally (up to 57 unit cells), the absolute values of the lowest transition energy

calculated with different techniques on the basis of different geometries do not differ significantly due

to the confinement of the charged species by the chain ends. Thus, these data cannot be exploited to

assess the best theoretical approach. The chain-length evolution of the transition energies is, however,

more sensitive to the choice of the theoretical approach when dealing with longer oligomers.

1.3.2 Optical Signature of Delocalized Interchain Polarons

The inherent disorder in organic conjugated polymers has long prevented the achievement of charge-

carrier mobilities compared to those in molecular crystals (see above) or amorphous silicon. However,

in the case of regioregular poly-3-hexylthiophene (RR-P3HT), self-organization of the polymer chains

leads to a lamellar structure with two-dimensional sheets built by strongly interacting conjugated

segments (with interchain distances on the order of 3.8 A); as a result, the material displays room-

temperature mobilities of up to 0.1 cm2=V s [58,59]. (Films of RR-P3HT were successfully used in an

FET device to drive a light-emitting diode (LED) based on a luminescent polymer, thereby providing the

first demonstration of an all-organic display pixel [59].) The large mobilities reported in the case of

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.03 4 5 6 7 8 9

BHandHLYP-TDDFT // AM1

INDO-SCI // AM1

INDO-SCI // AM1 neutral geom

BHandHLYP-TDDFT // VWN-BP

INDO-SCI // VWN-BP

Tran

sitio

n en

ergy

(eV)

Number of Ph ringsFIGURE 1.11 Evolution, as a function of the number of phenylene rings in the chains, of the energy of the lowest

optically allowed vertical transition in OPV radical-cations, as obtained by different procedures (the first acronym

represents the method used for the electronic-structure calculations and the second, that for the geometry

optimizations: AM1 and INDO are semiempirical HF methods, VWN-BP is a pure DFT functional, and BHandH-

LYP is a hybrid DFT with 50% of HF exchange).



RR-P3HT suggest that the transport mechanisms might be different in such a highly ordered polymer

and could involve charged species that are delocalized over several adjacent chains [58,59].

The nature of the charge carriers in RR-P3HT has been investigated experimentally using optical

charge modulation spectroscopy (CMS) [60] and photoinduced absorption (PiA) [61]. These studies

have pinpointed substantial differences between the optical signatures of polarons in the microcrystal-

line materials compared to chemically doped polythiophene in solution. Such differences were attrib-

uted to delocalization of the charges over several adjacent polythiophene chains, which is consistent with

the high mobilities within the two-dimensional conjugated sheets [58,59].

To assess the validity of these propositions, we investigated the influence of interchain charge

delocalization on the optical properties of singly charged conjugated systems. For the sake of simplicity

(the electronic excited states of phenylene-based molecules are less subject to configuration mixing than

in oligothiophenes), we focused our attention on a model phenylenevinylene oligomer, namely the

5-ring OPV, hereafter denoted 5PV. Ground state geometry optimizations of the isolated 5PV molecule

in its neutral and singly charged states have been carried out at the Austin Model 1=Full Configuration

Interaction (AM1=FCI) level (with four molecular orbitals included in the CI active space) [62].

Figure 1.12 shows the bond-length deformations associated with the formation of a positive molecular

polaron on 5PV. Charge injection induces the appearance of a slight quinoid character on the phenylene

0.05

0.04

0.03

0.02

0.01

0.00

PPV5 - P+ 1 chain2 chains

0 4 8 12 16 20 24 28 32 36 40Bond label

Bond

-leng

th d

efor

mat

ion

()

1

24

6

53

78

19

2022

24

2123 25

26 3941

4240

38

37

FIGURE 1.12 Differences (in A) between the AM1=FCI calculated bond lengths in the neutral and singly charged

states of 5PV, in the isolated molecule (black) and in the dimer (yellow). The structure and bond labeling of the

5-ring oligomer is shown at the bottom.



rings, together with a decrease in bond-length alternation in the vinylene linkages. These deformations are

more pronounced around the center of the molecule and typically extend over three repeat units (20 A).On the basis of the optimized geometry of the charged species, the one-electron energy levels were

calculated using both the AM1 and INDO [63] semiempirical approaches. A simplified representation of

the one-electron energy diagram typically obtained with these two techniques is given in Figure 1.13a

and has been discussed above.

The AM1-optimized geometry of the charged species is then used as input for the computation of the

excited states, which is performed at two different levels:

1. The AM1=FCI formalism, as adopted for geometry optimization, but considering a larger

configuration interaction expansion (including up to 16 molecular orbitals) to insure conver-

gence of the spectroscopic properties.

2. The INDO=SDCI method, in which all single excitations over the electronic p-levels and a

limited number of double excitations (more than 16 MOs) were involved.

As seen from Figure 1.14, most of the optical absorption cross section of the charged species is shared

between two excited states described as the C1 and C2 electronic transitions of Figure 1.13, namely the

singly excited HOMO!P1 and P1!P2 configurations, respectively [63].The influence of interchain interactions was assessed by considering a cofacial aggregate formed by

two 5PV chains separated by 4 A. This configuration is similar to that encountered in the microcrys-

talline domains of RR-P3HT [60]. When enforcing such a symmetric cofacial arrangement, the INDO

and AM1 approaches lead to molecular orbitals completely delocalized over the two conjugated chains,

which carry half a unitary charge each. To determine the ground state geometry of the two-chain system

in its singly oxidized state, we applied the same AM1=FCI approach as in the single chain case (while

doubling the active space to eight molecular orbitals for size consistency).

The lattice deformations in the aggregate, as provided by this approach, are compared to those

calculated for the isolated molecule in Figure 1.12. Since the perturbation induced by charge injection in

Energy

LUMO LUMO

HOMO

1 chain 2 chain

HOMO

P2 P2

P1

CT

C2C3

C3

C1

P2

P1

C2

(a) (b)

C1P1

au

bu

bu

au

auau

bg

bgbg

bg

ag

ag

FIGURE 1.13 Schematic representation of the one-electron energy diagram for a polaron: (a) localized on a single

conjugated chain; and (b) delocalized over two cofacial chains. The symmetry of the orbitals and the relevant

electronic excitations are indicated.



the individual chains of the dimer is weaker than in the single-chain case, the bond-length modifications

are less pronounced in the aggregate (especially around the center of the molecule) and extend in a

symmetric way over the two conjugated chains.

The electronic structure and absorption spectrum of the cationic dimer can be interpreted in the

framework of a two-site molecular (Holstein) polaron model (or equivalently, in terms of the Marcus

Hush model for self-exchange electron transfer). As mentioned in Section 1.2 and discussed in more

detail elsewhere [9], the system properties depend on the interplay between the electronic coupling

(transfer integral t between adjacent chains) and the reorganization energy l (polaron binding energy,

Epol l=2). In the case when the electronic coupling 2t is smaller than the reorganization energy l, thelower adiabatic potential surface exhibits two equivalent minima. Each of these minima corresponds to

the situation in which the system is mainly localized on one of the valence structures {Ma Mb} and{Ma Mb } (see Section 1.2), respectively. In terms of the Holstein model, this situation corresponds tothe formation of a localized molecular polaron. The electronic spectrum is characterized in this case by

the appearance in the visible or the near-infrared region of a charge-transfer band, with the band

maximum being equal to the reorganization energy: ECT l. In the case of strong electronic coupling(2t > l), corresponding to the situation discussed in this section, the lower potential surface possesses

only one minimum. In this case, the CT transition becomes a direct measure of the electronic coupling,

since: ECT 2t. In a one-electron picture, this band is related to the resonance splitting of the oligomerSOMO levels (P1). The interchain coupling leads to a similar resonance splitting of all other monomer

electronic levels (see Figure 1.13). As a result of C2h symmetry of the cofacial dimer configuration

considered here, all levels split into gerade=ungerade symmetry molecular orbital pairs. The appearance

of these levels leads to new optical transitions in the dimer. As shown in Figure 1.13, the low-energy

transitions involve the levels P1, P10, P2, and P20 referred to as polaronic levels in Section 1.2.The absorption spectrum of the cationic dimer, as computed at the AM1=FCI level (with up to

26 molecular orbitals in the active space) and INDO=SDCI (with all possible single excitations within

the p-manifold and double excitations over 22 p-orbitals), is shown in comparison to that of the

one-chain polaron in Figure 1.14. The optical features discussed below are common to the descriptions

provided by the AM1=FCI and INDO=SDCI formalisms.

The CT band (Figure 1.14) is predicted to be around 0.1 [0.25] eV at the AM1=FCI [INDO=SDCI]

level. This result indicates that the interchain electronic coupling is about 400 [1000] cm1, i.e.,comparable to the values derived for pentacene and rubrene (see Section 1.2) at Koopmans theorem

level. The CT transition is polarized along the interchain packing

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